Multi-dimensional sensors, such as magnetometers and accelerometers, are increasingly used in mobile applications for location or orientation awareness. For example, a tilt compensated digital compass may be used in applications such as pedestrian navigation. A tilt compensated digital compass includes a three-dimensional magnetometer to measure the Earth's magnetic field and a three-dimensional accelerometer for tilt compensation.
Mobile applications typically require compact and low power components. Current electro-mechanical (MEM) type magnetometers and accelerometers fulfill these requirements and are accurate and reliable. The main challenge in incorporating magnetometers and accelerometers, such as that used in a tilt compensated digital compass, into mobile devices, is calibration of the sensors.
One article that discusses calibration of a multi-dimensional sensor, in particular a magnetometer, is entitled “Extension of a Two Step Calibration Methodology to Include Non-Orthogonal Sensors”; C. C. Foster, G. H. Elkaim; IEEE Transactions on Aerospace and Electronic Systems, July 2008, p. 1070-78, which is incorporated herein by reference. This article, however, does not discuss how to map ellipse and ellipsoid parameters to sensor calibration parameters (offsets, sensitivities, non-orthogonalities). These parameters are needed to convert raw sensor data to calibrated sensor data.
Mobile applications in which a sensor may be found, e.g., such as a cellular telephone, are mass produced and, thus, the multi-dimensional sensors cannot be factory-calibrated individually as is the case with more specialized equipment as the cost would be prohibitive. Accordingly, auto-calibration of multi-dimensional sensors is desired.